64 resultados para 230101 Mathematical Logic, Set Theory, Lattices And Combinatorics


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This article looks to three inspirational Black women, bell hooks, Stacey McBride-Irby and Patricia Williams, in the pursuit of radical curriculum. While today curriculum is critiqued as racialized, gendered, sexualised and classed, the formats of curriculum documents such as text books, units of work and lesson plans have changed little. These documents are often conceived as linear sequences of steps leading to outcomes, and their voices are distanced and “neutral”. Drawing on a doctoral study of curriculum design in Australia, this article embraces a different approach by opening up a unit of work on girls’ popular culture to hooks’ invocations to teach to transgress, so that curriculum might be experienced as colour and curves, rather than a monochrome route to a pre-determined end point. Through this, along with hooks, I invite teachers to live pedagogy, rather than to deliver it.

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The outcome from this project produces a database of over 185 projects and 726 publications relating to numeracy research to systematically ‘mapped’ Australian research on primary school numeracy over the last decade. The database incorporates research summaries and findings that are easily accessible to teachers and teacher educators, and act as a valuable tool for determining further research directions. The project report examines the available research and organises the discussion of the research findings under a set of themes and sub-themes.

Some summarised examples from the report reveals that:

* Effective teachers of numeracy:
- have high expectations of their students;
- focus on children’s mathematical learning, rather than on providing pleasant classroom experiences;
- provide a challenging curriculum;
- use higher-order questioning;
- make connections both within mathematics and between mathematics in different contexts; and
- use highly interactive teaching involvement with students in class discussion.

* Effective professional development programmes:
- provide teachers with the time and appropriate resources to enable them to reflect on their teaching;
- provide continuing support and encouragement while teachers explore possibilities and trial new strategies in their classrooms;
- involve teachers in school-based and wider networks;
- are of sufficient duration to allow significant changes to habitual beliefs and practices; and
- create opportunities for the exploration of theory-practice relationships.

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It has been recognised that formal methods are useful as a modelling tool in requirements engineering. Specification languages such as Z permit the precise and unambiguous modelling of system properties and behaviour. However some system problems, particularly those drawn from the information systems problem domain, may be difficult to model in crisp or precise terms. It may also be desirable that formal modelling should commence as early as possible, even when our understanding of parts of the problem domain is only approximate. This thesis suggests fuzzy set theory as a possible representation scheme for this imprecision or approximation. A fuzzy logic toolkit that defines the operators, measures and modifiers necessary for the manipulation of fuzzy sets and relations is developed. The toolkit contains a detailed set of laws that demonstrate the properties of the definitions when applied to partial set membership. It also provides a set of laws that establishes an isomorphism between the toolkit notation and that of conventional Z when applied to boolean sets and relations. The thesis also illustrates how the fuzzy logic toolkit can be applied in the problem domains of interest. Several examples are presented and discussed including the representation of imprecise concepts as fuzzy sets and relations, system requirements as a series of linguistically quantified propositions, the modelling of conflict and agreement in terms of fuzzy sets and the partial specification of a fuzzy expert system. The thesis concludes with a consideration of potential areas for future research arising from the work presented here.

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This paper presents a method for conducting dynamic due diligence to evaluate Mergers and Acquisitions; demonstrates its effectiveness in a particular case; and extrapolates its theoretical and practical implications to the general case. It may be called the ‘ECIPP’ method - an acronym for: Establishing mandates; Creating projections; Identifying issues; Prioritizing procedures and Performing them.

Two established alternative due diligence methods are examined. The prevailing finance-theory-based procedure has the virtues of simplicity and elegance; the vice is abstraction. The prevailing practitioner-based regime has the virtues of thoroughness and concreteness but the vices of rigidity and inefficiency. Resolving the tradeoffs inherent in both static prescriptions provides an opportunity for a dynamic, innovative approach derived from grounded theory and an application of Hindle’s (1993) theory of venture renaissance through application of an enhanced paradigm of Entrepreneurial Business Planning. The ECIPP method retains simplicity, concreteness and thoroughness but eliminates abstraction, rigidity and inefficiency.

This is demonstrated in a case. ChildCo’s CEO had only one month to complete his M&A evaluation; no expertise or previous experience; severely limited budget for the exercise and had been flatly informed by prevailing M&A experts that what he wanted could not be done. Using the ECIPP method, the CEO and the author did it: on time, within budget and to the satisfaction of a previously skeptical board of one of the world’s largest multi-national companies including arguably the world’s most professional corporate M&A division.

The replicability logic of the case research permits two generalisations. (1) ECIPP extends the range and utility of Entrepreneurial Business Planning as a management technology, well beyond the constraints to which it is usually confined. (2) The ECIPP method of dynamic due diligence is an innovation worthy of mature consideration and further investigation by theorists and practitioners in the M&A field, in the disciplines of both Finance and Entrepreneurship and, well beyond, in the realms of general management theory, methodology and practice.

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The Commission on Graduate Education in Economics had raised several concerns regarding the role of mathematics in graduate training in economics (Krueger, 1991; Colander, 1998, 2005). This paper undertakes a detailed scrutiny of the notion of a utility function to motivate and describe the common patterns across mathematical concepts and results that are used by economists. In the process one arrives at a classification of mathematical terms which is used to state mathematical results in economics. The usefulness of the classification scheme is illustrated with the help of a discussion of Arrow's impossibility theorem. Common knowledge of the patterns in mathematical concepts and results could be effective in enhancing communication between students, teachers and researchers specializing in different sub-fields of economics.

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This paper deals with the problem ofstructuralizing education and training videos for high-level semantics extraction and nonlinear media presentation in e-learning applications. Drawing guidance from production knowledge in instructional media, we propose six main narrative structures employed in education and training videos for both motivation and demonstration during learning and practical training. We devise a powerful audiovisual feature set, accompanied by a hierarchical decision tree-based classification system to determine and discriminate between these structures. Based on a two-liered hierarchical model, we demonstrate that we can achieve an accuracy of 84.7% on a comprehensive set of education and training video data.

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The research reported in this paper examined spoken mathematics in particular well-taught classrooms in Australia, China (both Shanghai and Hong Kong), Japan, Korea and the USA from the perspective of the distribution of responsibility for knowledge generation in order to identify similarities and differences in classroom practice and the implicit pedagogical principles that underlie those practices. The methodology of the Learner’s Perspective Study (LPS) documented the voicing of mathematical ideas in public discussion and in teacher-student conversations and the relative priority accorded by different teachers to student oral contributions to classroom activity. Significant differences were identified among the classrooms studied, challenging simplistic characterisations of ‘the Asian classroom’ as enacting a single pedagogy, and suggesting that, irrespective of cultural similarities, local pedagogies reflect very different assumptions about learning and instruction. We have employed spoken mathematical terms as a form of surrogate variable, possibly indicative of the location of the agency for knowledge generation in the various classrooms studied (but also of interest in itself). The analysis distinguished one classroom from another on the basis of “public oral interactivity” (the number of utterances in whole class and teacher-student interactions in each lesson) andmathematical orality” (the frequency of occurrence of key mathematical terms in each lesson). Classrooms characterized by high public oral interactivity were not necessarily sites of high mathematical orality. In particular, the results suggest that one characteristic that might be identified with a national norm of practice could be the level of mathematical orality: relatively high mathematical orality characterising the mathematics classes in Shanghai with some consistency, while lessons in Seoul and Hong Kong consistently involved much less frequent spoken mathematical terms. The relative contributions of teacher and students to this spoken mathematics provided an indication of how the responsibility for knowledge generation was shared between teacher and student in those classrooms. Specific analysis of the patterns of interaction by which key mathematical terms were introduced or solicited revealed significant differences. It is suggested that the empirical investigation of mathematical orality and its likely connection to the distribution of the responsibility for knowledge generation are central to the development of any theory of mathematics instruction.

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The importance of local news is gaining traction with industry and in journalism scholarship. But there is a need for careful analysis of what it means to be “local” and how we might theorise the role and place of news organisations and journalists who serve local audiences. This paper draws on three qualitative case studies of local newspapers serving small towns and cities in Australia to generate concepts that can be used to deepen understanding about this form of news. Our research highlights that to be local is practical and embodied. It requires individuals, groups, organisations or institution to be anchored in a particular locale and have in-depth understanding of that place that has developed over time. We extend the scholarship of Pierre Bourdieu to suggest this may be understood as local habitus—a powerful set of dispositions and practical logic developed within a place—that the small newspaper is inherently tied to. Reading a newspaper is part of one's local habitus while an individual who possesses it in the journalistic field may have a significant advantage in their day-to-day practices. We suggest this theoretical lens can offer rich insights into the future of local news production across the western world.

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While comparative law has become a key discipline, its instrumentalist use has turned out to be a powerful weapon: it is the ‘pen’ by which the identity of and differences in law’s geopolitics are continually written and rewritten. Given its attractive functionalist essence, comparative law is gaining increasing international credit as a way of developing newer theories of sovereignty and governance in a framework in which law is conceived of less as a set of rules and more as a symbolic vestimentum of global soft power. The present contribution critically investigates the relationship between distortive views of comparative law’s geopolitics and the intimate essence of the doctrine aimed at creating the ‘aspatial’, unbounded, illimitable (and hence intangible) liberal global order whose governance appears to transcend the idea and form(s) of law through which the ‘politicization’ and ‘juridification’ of modernity have been achieved in the last century. In doing so, it also addresses why such an alliance has made it easier to ‘discover’ and ‘sell’ the smooth and rectilinear land of the figuratively unspoken and unwritten as the terra incognita that lies over what is created by the constructivist political intervention(s) of the modern nation-state

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Wireless mesh networks are widely applied in many fields such as industrial controlling, environmental monitoring, and military operations. Network coding is promising technology that can improve the performance of wireless mesh networks. In particular, network coding is suitable for wireless mesh networks as the fixed backbone of wireless mesh is usually unlimited energy. However, coding collision is a severe problem affecting network performance. To avoid this, routing should be effectively designed with an optimum combination of coding opportunity and coding validity. In this paper, we propose a Connected Dominating Set (CDS)-based and Flow-oriented Coding-aware Routing (CFCR) mechanism to actively increase potential coding opportunities. Our work provides two major contributions. First, it effectively deals with the coding collision problem of flows by introducing the information conformation process, which effectively decreases the failure rate of decoding. Secondly, our routing process considers the benefit of CDS and flow coding simultaneously. Through formalized analysis of the routing parameters, CFCR can choose optimized routing with reliable transmission and small cost. Our evaluation shows CFCR has a lower packet loss ratio and higher throughput than existing methods, such as Adaptive Control of Packet Overhead in XOR Network Coding (ACPO), or Distributed Coding-Aware Routing (DCAR).

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This paper provides an analysis of student experiences of an approach to teaching theory that integrates the teaching of theory and data analysis. The argument that supports this approach is that theory is most effectively taught by using empirical data in order to generate and test propositions and hypotheses, thereby emphasising the dialectic relationship between theory and data through experiential learning. Bachelor of Commerce students in two second-year substantive organisational theory subjects were introduced to this method of learning at a large, multi-campus Australian university. In this paper, we present a model that posits a relationship between students' perceptions of their learning, the enjoyment of the experience and expected future outcomes. The results of our evaluation reveal that a majority of students:

•enjoyed this way of learning;
•believed that the exercise assisted their learning of substantive theory, computing applications and the nature of survey data; and
•felt that what they have learned could be applied elsewhere.

We argue that this approach presents the potential to improve the way theory is taught by integrating theory, theory testing and theory development; moving away from teaching theory and analysis in discrete subjects; and, introducing iterative experiences in substantive subjects.

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Eased on field observations and compilation of data, a new stratigraphic concept, herein named the Permian-Triassic boundary stratigraphic set (PTBST), is proposed. The PTBST consists of, in ascending order, beds of claystone, limestone (or marl) and claystone. This boundary stratigraphic
set has been recognized at many sections in the Yangtze region of South China, with laterally stable lithological characters, the same or comparable biotas, comparable radiometric ages, and identical or similar magnetostratigraphic and chemostratigraphic signals. Therefore, the PTBST marks an isochronous unit and can serve as an important and effective marker set for regional and global correlations.
The important index fossils for the lowermost Triassic, Hindeodus parvus or Claraia, may be diachronous in their first occurrences with respect to the base of the PTBST and, therefore, should not be used as an exclusive indicator for the beginning of the Triassic. Rather more attention should
be paid to events, succession of events and/or event surfaces, which would potentially provide a more precise tool for high-resolution stratigraphic division and correlation.

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Purpose – Pareto’s Law often refers to the theory that a small percentage of a total is responsible for a large proportion of the total outcome. It is commonly known as the 80/20 law or principle. The objective is to review and debate whether there is a “Pareto syndrome” in the distribution of crucial research and journal criteria in top marketing journals.

Design/methodology/approach –
The authors provide a review and a debate based upon previous research on top marketing journals. For this purpose, the Pareto syndrome concept is introduced, based upon a set of research and journal criteria. Their distribution is examined.

Findings –
The review of research and journal criteria in top marketing journals generated an extremely skewed outcome. When it comes to the criteria, the top journals in marketing tend to be governed by narrow concerns of research rather than broad ones.

Research limitations/implications –
The research and journal criteria that have a skewed outcome may reinforce the rigidity and the lack of innovativeness of the marketing discipline. The evolutionary speed of the discipline may at best be reduced or it may at worst grind to a halt. The authors argue that there are a number of serious concerns to be addressed in the future review and debate of top journals in marketing.

Practical implications –
Editors and editorial boards need seriously to address the concerns reviewed and debated, namely the skewed distribution of criteria, such as affiliation, data and methodology.

Originality/value –
The authors debate that there is evidence that confirms the existence of a Pareto plus syndrome in key research and journal criteria of top marketing journals.

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Computerized clinical guidelines can provide significant benefits to health outcomes and costs, however, their effective implementation presents significant problems. Vagueness and ambiguity inherent in natural (textual) clinical guidelines is not readily amenable to formulating automated alerts or advice. Fuzzy logic allows us to formalize the treatment of vagueness in a decision support architecture. This paper discusses sources of fuzziness in clinical practice guidelines. We consider how fuzzy logic can be applied and give a set of heuristics for the clinical guideline knowledge engineer for addressing uncertainty in practice guidelines. We describe the specific applicability of fuzzy logic to the decision support behavior of Care Plan On-Line, an intranet-based chronic care planning system for General Practitioners.

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k-nearest neighbors (kNN) is a popular method for function approximation and classification. One drawback of this method is that the nearest neighbors can be all located on one side of the point in question x. An alternative natural neighbors method is expensive for more than three variables. In this paper we propose the use of the discrete Choquet integral for combining the values of the nearest neighbors so that redundant information is canceled out. We design a fuzzy measure based on location of the nearest neighbors, which favors neighbors located all around x.